Wednesday, April 30, 2008

[AD 16] Effect of microstep rate on MSD and PSD

If the Poisson statistics is combined with the s*d process, the VAC depends on the system parameters as follows:

C_{vv}(m)=\frac{w_1^2}{\Delta t^2}\left[\frac{1/4}{1+|m|^{2-\beta}}\right]\left[\lambda^2\!+\!\delta_{m,0}\;\lambda\right]
While w_1 merely affects the scale of correlated bead fluctuations, the number of microsteps lambda per discretization intervall enters non-linearly into the formula.

The following plot shows the effect of lambda on the MSD:

And, even more pronounced, on the PSD:

The parameters were as follows:

sigN2=0.5e-4; // variance of white noise [um^2]
beta=1.5; // PL exponent of MSD [1]
lambda=2.0; // aver. nr. of microsteps per dT [1]
w1=5.0e-3; // width of single microstep [um]

It is inctructive to compare this with the effect of changing w1 at fixed lambda. The MSD:

The PSD:

Obviously, the effects are rather similar. This comes in handy, when lambda is adjusted to fit the experimental kurtosis. Then the simultaneous changes in the MSD/PSD can be compensated via w_1.

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